The dynamics of calcium in the cortical cytoplasm of plant cells has been modeled by Goodwin & Trainor (1985) using a mechanochemical field theory based on the interaction between calcium ions and the cytoskeleton. The resulting mathematical model is a system of two non-linear partial differential equations which rule the evolution of the free calcium concentration and of the cytogel strain field in the cytoplasm. According to the values of parameters such as: calcium diffusion coefficient, strength of the calcium-strain coupling, (...) gel elasticity or total calcium concentration, this system may be stable or unstable around an homogeneous equilibrium state. With the aid of numerical simulations, various kinds of solutions have been observed. When inertial forces ar neglected or for low values of the gel density, most of the solutions are asymptotically stable and are reached after a more or less complex transient. But for higher values of the volumetric density more complex solutions may exist, periodic in time and space or eventually chaotic. (shrink)

The growth of the vein system of the leaf ofTropaeolum peltophorum was studied at the vein level and at the limb level.The vein growth kinetics depend on the position of the vein on the leaf: there is a proximal/distal gradient and a bilateral gradient of the growth parameters. The growth field of the veins is also dependent on time and on vein position.Specific correspondences exist between singular points of the global growth curves, the variations of the growth field and the (...) vein position. The spatio-temporal organization of the vein system growth is then characterized by positional variations of kinetic order which show the existence of areal morphogenetic dissymmetry. (shrink)

The growth of the vein system of the leaf ofTropaeolum peltophorum was studied (i) at the vein level (analysis of the growth kinetics and of the growth field of the 7 primary veins) and (ii) at the limb level (comparison of the growth of the veins).The vein growth kinetics depend on the position of the vein on the leaf: there is a proximal/distal gradient and a bilateral gradient of the growth parameters (=variation of the temporal organization of the kinetics). The (...) growth field of the veins (=local growth pattern) is also dependent on time and on vein position. (shrink)